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| Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces |
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Citation： |
Xiaoli FU,Yan MENG,Dachun YANG.Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces[J].Chinese Annals of Mathematics B,2007,28(1):67~80 |
| Page view： 1136
Net amount： 891 |
Authors： |
Xiaoli FU; Yan MENG;Dachun YANG |
Foundation： |
Project supported by the National Natural Science Foundation of China (No. 10271015) and the Program for New Century Excellent Talents in Universities of China (No. NCET-04-0142). |
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| Abstract： |
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calder′on-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H^1(μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measure μ is the d-dimensional Lebesgue measure. |
Keywords： |
Commutator, Lipschitz function, Lebesgue space, Hardy space, RBMO space, Non-doubling measure |
Classification： |
47B47, 42B20 |
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